Real-time kd-tree construction on graphics hardware

ABSTRACT

Described is a technology for constructing kd-trees on GPUs, in a manner that is sufficiently fast to achieve real-time performance by exploiting GPU-based parallelism during the kd-tree construction. Tree nodes are built in breadth-first search order, e.g., to use a thread for each node at each level. For large nodes at upper tree levels, computations are parallelized over geometric primitives (instead of nodes). To this end, large nodes are split into child nodes by cutting off empty space based until an empty space ratio is achieved, and thereafter performing spatial splitting. Small nodes are split based on split candidate costs, e.g., computed by a surface area heuristic or a voxel volume heuristic (VVH).

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is related to copending U.S. patent application Ser. Nos. 12/241,046 and 12/241,044, hereby incorporated by reference.

BACKGROUND

A kd-tree(short for k-dimensional tree) is a well-known space-partitioning data structure for organizing points in k-dimensional space. As an acceleration structure, kd-trees have been used in a variety of graphics applications.

Because of its significant usage in graphics, fast kd-tree construction has been a subject of much interest in recent years, with several CPU-based algorithms proposed and/or implemented. However, real-time construction of kd-trees on the GPU was heretofore an unsolved problem.

SUMMARY

This Summary is provided to introduce a selection of representative concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used in any way that would limit the scope of the claimed subject matter.

Briefly, various aspects of the subject matter described herein are directed towards a technology by which a kd-tree is built via graphics hardware-based parallel processing, including by building nodes of the kd-tree in breadth-first search order, and differentiating between large nodes and small nodes while building the tree. For large nodes at upper tree levels, computations are parallelized over geometric primitives (instead of nodes). To this end, large nodes are split into sub-nodes (e.g., child nodes) by cutting off empty space based until an empty space ratio is achieved, and thereafter performing spatial splitting. Small nodes are split based on split candidate costs, e.g., computed by a surface area heuristic or a voxel volume heuristic (VVH).

In one aspect, for small nodes, triangle sets for candidates are represented as bitmasks. The bitmasks can be processed to compute costs, and also so sort geometric primitives/triangles.

Other advantages may become apparent from the following detailed description when taken in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which:

FIG. 1 is a block diagram representing example components of a kd-tree construction mechanism (builder) that builds kd trees via graphics processing hardware.

FIG. 2 is a flow diagram representing general steps of a kd-tree construction mechanism.

FIG. 3 is a flow diagram representing general steps of an algorithm for kd-tree construction.

FIGS. 4 and 5 are example representations of splitting a large node, including by cutting off empty space (FIG. 4) and by a spatial median split (FIG. 5).

FIG. 6 is a flow diagram representing general steps of an algorithm for large node processing.

FIG. 7 is a flow diagram representing general steps of an algorithm for small node preprocessing.

FIG. 8 is a flow diagram representing general steps of an algorithm for small node processing.

FIGS. 9 and 10 are example representations of storing triangle sets as bitmasks for a small root, including splitting a node (FIG. 9) into subsets of triangles for storing as bitmasks (FIG. 10).

FIG. 11 is a flow diagram representing general steps of a preorder traversal algorithm.

FIG. 12 shows an illustrative example of a computing environment into which various aspects of the present invention may be incorporated.

DETAILED DESCRIPTION

Various aspects of the technology described herein are generally directed towards a mechanism (e.g., including a set of algorithms) for constructing kd-trees on a graphics processing unit (GPU). Real-time performance is achieved by exploiting the GPU's streaming architecture at various stages of kd-tree construction. As will be understood, this is possible by building tree nodes completely in breadth-first search order, unlike previous parallel kd-tree algorithms.

This provides a real-time kd-tree algorithm on a GPU, with kd-trees having comparable quality to those constructed by off-line CPU algorithms, but in a manner that is significantly faster than well-optimized single-core CPU algorithms, yet competitive with multi-core CPU algorithms. The algorithm provides a general way for handling dynamic scenes on the GPU.

Some of the examples herein describe an implementation of a kd-tree builder based on NVIDIA Corporation's CUDA framework. CUDA provides a general-purpose C language interface for GPU programming, and also exposes hardware features which are useful for data-parallel computations. For example, it allows arbitrary gather and scatter memory access from GPU programs, as generally mentioned herein. For example, during kd-tree construction, some of the data is stored as dynamic lists in linear device memory allocated via CUDA; list size is doubled whenever more memory is required. This allows avoiding overhead in CUDA memory management after an initial run, at the cost of more memory consumption. For structures with many fields such as nodes and triangles, structure of arrays (SoA) instead of array of structures (AoS) are used for more optimal GPU cache performance. Further, parallel primitives such as reduce and scan are called in the example implementation, which are implemented.

Notwithstanding, it is understood that these are only examples, and the technology described herein may be implemented in other environments. As such, the present invention is not limited to any particular embodiments, aspects, concepts, structures, functionalities or examples described herein. Rather, any of the embodiments, aspects, concepts, structures, functionalities or examples described herein are non-limiting, and the present invention may be used various ways that provide benefits and advantages in computing and graphics processor computations in general.

Turning to FIG. 1, there is shown a general block diagram showing how the kd-tree construction mechanism 102 may be used by an application 104 (which may be an operating system component). In general, the application 104 calls an API or the like to build a kd-tree 106 based on supplied information to the kd-tree construction mechanism 102. The kd-tree construction mechanism 102 provides code and data for execution in the GPU 108, which executes the code to build the kd-tree 106.

In designing the kd-tree mechanism 102 (e.g., the algorithm set) for the GPU 108, the GPU's streaming architecture is leveraged when parallelizing kd-tree construction. Contemporary GPUs are substantially parallel, typically requiring over one-hundred threads for optimal performance. By following breadth-first search order, at each breadth-first search step, every node at the same tree level spawns a new thread and the total number of threads doubles from the preceding step.

To maintain kd-tree quality, schemes for fast evaluation of node split costs are provided, e.g., the efficient calculation of node split costs, such as the surface area heuristic (SAH) and voxel volume heuristic (VVH) costs are considered. The standard practice of precisely evaluating the costs for the tree nodes is prohibitively expensive for real-time techniques. To address this issue, different schemes for the so-called “large” and “small” nodes are described herein, wherein a node is deemed as large if the number of triangles in the node is greater than a user-specified threshold otherwise it is small (e.g., one such threshold for large/small node is set as T=64). As described below, for large nodes at upper tree levels, two heuristics are used to estimate the costs, namely median splitting and “empty space maximizing.” For small nodes near the bottom of the tree, where exact evaluation of the costs is necessary, a data structure is provided for storing the geometry primitives in these nodes as bitmasks, which allows efficiently evaluation of the exact costs, as well as sorting these primitives using bitwise operations.

By way of one example of GPU-based kd-tree construction, an example of building SAH kd-trees, such as for ray tracing on the GPU, is described. The adaption of the algorithm to other kinds of kd-trees is straightforward. As with conventional kd-tree construction algorithms, the technique described herein builds a kd-tree in a greedy, top-down manner by recursively splitting the current node into two subnodes as in FIG. 2. Step 202 evaluates the SAH costs for splitting plane candidates, followed by step 204 which picks the optimal candidate with the lowest cost. The node is then split into two child nodes at step 206. Step 208 sorts triangles and distributes them to the two children.

The SAH cost function is defined as:

${{{SAH}(x)} = {C_{ts} + \frac{{C_{L}(x)}{A_{L}(x)}}{A} + \frac{{C_{R}(x)}{A_{R}(x)}}{A}}},$ where C_(ts) is the constant cost of traversing the node itself, C_(L)(x) is the cost of the left child given a split position x, and C_(R)(X) is the cost of the right child given the same split. A_(L)(X) and A_(R)(X) are the surface areas of the left and right child respectively, and A is the surface area of the node. Note that C_(L)(x) and C_(R)(X) can only be evaluated after the entire sub-tree has been built. Instead of seeking a globally optimal solution, existing algorithms use a locally greedy approximation by assuming the children are leaf nodes. In this case C_(L)(x) and C_(R)(X) equal the number of elements contained in the left and right child respectively.

The algorithm takes triangles as input and follows the construction pipeline as shown in FIG. 3 and set forth below:

Algorithm 1, Kd-Tree Construction:

// initialization stage nodelist ← new list activelist ← new list smalllist ← new list nextlist ← new list Create rootnode activelist.add(rootnode) for each input triangle t in parallel  Compute AABB for triangle t // large node stage while not activelist.empty( )  nodelist.append(activelist)  nextlist.clear( )  PROCESSLARGENODES(activelist, smalllist, nextlist)  Swap nextlist and activelist // small node stage PREPROCESSSMALLNODES(smalllist) activelist ← smalllist while not activelist.empty( )  nodelist.append(activelist)  nextlist.clear( )  PROCESSSMALLNODES(activelist, nextlist)  Swap nextlist and activelist // kd-tree output stage PREORDERTRAVERSAL(nodelist)

After an initialization step (step 302), the algorithm builds the tree in a breadth-first search manner, for both large nodes and small nodes. Then, the nodes of the tree are reorganized and stored. The pipeline comprises a set of stream processing steps together with some coordination work. The streaming steps are done on the GPU, while coordination work is done on the CPU (at relatively negligible costs).

In the initialization stage (step 302), global memories are allocated for tree construction and the root node is created. Additionally, at step 306 streaming step is performed to compute the axis-aligned bounding box (AABB) for each input triangle (in parallel, via steps 304, 307 and 308). In one current implementation, the user-specified threshold for large/small node is set as T=64.

As mentioned above, the SAH evaluation in a conventional greedy optimization algorithm assumes that the current split produces two leaf nodes. For large nodes, this assumption is almost always untrue, whereby the resulting estimation is far from accurate. The splitting scheme described herein for large nodes is a combination of spatial median splitting and “empty space maximizing,” which is effective for the upper levels of the tree. More particularly, if the empty space contained in the current node is larger than a predefined ratio C_(e) along one axis, the empty space is cut off in the next split, as generally represented in FIG. 4; otherwise, the split plane is chosen at the spatial median of the node's longest axis split, as generally represented in FIG. 5. One current implementation takes C_(e) equal to twenty five percent. Note that to apply this splitting scheme, a tight bounding box of the triangles contained in the node is computed.

Described herein is a strategy for large nodes at upper tree levels so as to further leverage the large scale parallelism of GPUs. For these nodes, the mechanism parallelizes the computation over geometric primitives instead of nodes at each level. This strategy is effective because there are only a relatively small number of large nodes at the upper levels, especially near the top of the tree, (which makes parallelizing over nodes inefficient and leaves the massive parallelism of GPUs underexploited). Moreover, the workload among threads is likely to be unbalanced because the number of primitives may vary significantly from node to node.

One suitable large node processing procedure, PROCESSLARGENODES, is set forth in Algorithm 2 and is also generally represented in FIG. 6:

Algorithm 2, Large Node Stage—PROCESSLARGENODES:

procedure PROCESSLARGENODES(   in activelist:list;   out smalllist, nextlist:list) begin  // divide triangles into chunks  for each node i in activelist in parallel   Divide all triangles in node i into fixed size chunks, store   chunks in chunklist  // compute per-node bounding box  for each chunk k in chunklist in parallel   Compute the bounding box of all triangles in k, using standard   reduction  Perform segmented reduction on per-chunk reduction result to  compute per-node bounding box  // split large nodes  for each node i in activelist in parallel   for each side j of node i    if i contains more than C_(e) empty space on     side j then      Cut off i's empty space on side j   Split node i at spatial median of the longest axis   for each created child node ch    nextlist.add(ch)  // sort and clip triangles to child nodes  for each chunk k in chunklist in parallel   i ← k.node( )   for each triangle t in k in parallel    if t is contained in both children of i then     t₀ ← t     t₁ ← t     Sort t₀ and t₁ into two child nodes     Clip t₀ and t₁ to their respective owner node    else     Sort t into the child node containing it  // count triangle numbers for child nodes  for each chunk k in chunklist in parallel   i ← k.node( )   Count triangle numbers in i's children, using reduction  Perform segmented reduction on per-chunk result to compute  per-child-node triangle number  // small node filtering  for each node ch in nextlist in parallel   if ch is small node then    smalllist.add(ch)    nextlist.delete(ch) end

This procedure takes activelist as input, and updates smallist and nextlist as output. Note that a triangle-node association list is also maintained for each node list. The triangle-node association list stores triangle indices contained in the node list, sorted by node index. Each node in the node list records the index of its first triangle in the triangle-node association list and the triangle number it contains, the scene space it occupies, and the pointers to its child nodes.

FIG. 6 describes the general steps of the above algorithm. A first step (step 602) of the procedure divides the triangles in each node into fixed-sized chunks. In one implementation, the chunk size is set to N=256. A large fraction of the subsequent computations are parallelized over the triangles in these chunks.

In a second step (step 604), the bounding box of the triangles in each node is computed. This is done by first computing the bounding box of the triangle's AABBs in each chunk using a reduction algorithm (described below with respect to Algorithm 3), and then computing the bounding boxes of the nodes by performing segmented reduction in a known manner on the sequence of the chunk reduction results. Segmented reduction performs reduction on arbitrary segments of an input sequence. The result is a sequence in which each element holds the reduction result of one segment.

One suitable GPU algorithm for GPU segmented reduction is described in Algorithm 3:

procedure GPUSEGREDUCE(   in data, owner:list; op: reduction operator;   out result:list) begin  result ← new list  Fill result with op's identity element  // assume there are n elements  for d = 0 to log₂ n − 1   for each i = 0 to (n − 1)/2^(d+1) in parallel    w₀ ← owner[2^(d+1)i]    w₁ ← owner[2^(d+1)i + 2^(d)]    if w₀ ≠ w₁ then     result[w₁] ← op(result[w₁], data[2^(d+1)i + 2^(d)])    else     data[2^(d+1)i] ← op(data[2^(d+1)i], data[2^(d+1)i + 2^(d)]) end

In the input list data, the data elements belonging to the same segment are located contiguously. In another input list owner, owner[i] indicates the segment index of data[i]. The reduction operator op is associated with an identity value, as listed in the table below:

Operator Identity value Usage min +∞ compute bounding box max −∞ compute bounding box + 0 count triangle number

The algorithm takes a multi-pass approach. Each thread takes two elements. If the two elements have the same owner, they are replaced by their operation result. Otherwise, one element is accumulated into result and the other is retained. Note that the chunk data structure is related to optimal performance. Within each chunk, only unsegmented reduction is performed on the triangles' axis-aligned bounding boxes, significantly reducing the element number in the subsequent segmented reduction. Although it is possible to compute the node bounding boxes by performing segmented reduction on the input triangles' axis-aligned bounding boxes directly, this is inefficient because large segmented reductions are about three times slower than large unsegmented reductions.

In a third step, (step 606), with computed node bounding boxes, large nodes are split in parallel using the splitting scheme described above. Note that a node is repeatedly split using empty space splitting until a spatial median split is reached. This allows reusing the bounding box and avoiding unnecessary computations after empty space splitting.

In a fourth step, (step 608), triangles are sorted and clipped into child nodes. Triangle sorting is essentially list splitting. For each chunk, the triangles in the chunk are first checked to generate a vector of Boolean values, which indicates whether each triangle is in a child node or not. Then the triangles are divided into two groups, with the triangles marked true on the left side of the output vector and the triangles marked false on the right side. This can be easily done using a known split operation. For those triangles contained in both child nodes, another pass is needed to clip them into the nodes. In another step, step 610, the triangle numbers for the child nodes are counted using segmented reduction in a way similar to bounding box computation. The reduction operator used here is “+”. To filter small nodes, if the triangle number of a node is less than the threshold T, it is added to smalllist and deleted from nextlist, as generally represented by step 612.

Compared to the large node stage, the small node stage is relatively simple. First, the computation is parallelized over nodes rather than triangles. The workload among small nodes is naturally balanced because the triangle numbers of small nodes do not vary significantly (from 0 to T). Second, unlike in the large node stage, triangles are not clipped when splitting small nodes. Although clipping triangles to owner nodes reduces false positives of the triangle-in-node test and reduces the SAH cost, clipping may also cause undesirable excessive splits because SAH does not take memory costs into account. While clipping is effective for large nodes by preventing false positives from accumulating over future splits, for small nodes, actual experiments indicate that clipping rarely improves ray tracing performance. Thus triangles are not clipped for small nodes, and the splitting plane candidates are restricted to those determined by the faces of the axis-aligned bounding boxes of triangles contained in the initial small nodes.

As shown in Algorithm 4 and as generally represented in FIGS. 7 and 8, the small node stage comprises two procedures, PREPROCESSSMALLNODES (FIG. 7) and PROCESSSMALLNODES (FIG. 8):

procedure PREPROCESSSMALLNODES(smalllist:list;) begin  for each node i in smalllist in parallel   i.splitList ← list of all split candidates in i   for each split candidate j in i in parallel    /* “left” represents smaller coordinate */    j.left ← triangle set on the left of j    j.right ← triangle set on the right of j end procedure PROCESSSMALLNODES(   in activelist:list;   out nextlist:list) begin  for each node i in activelist in parallel   // compute SAH and determine the split plane   s ← i.triangleSet   r ← i.smallRoot   A₀ ← area of node i   SAH₀ ←|| s ||   for j where j ε r.splitList and j.triangle ε s    C_(L) ←|| s ∩ j.left ||    C_(R) ←|| s ∩ j.right ||    A_(L) ← area of left child after split j    A_(R) ← area of right child after split j    SAH_(j) ← (C_(L)A_(L) + C_(R)A_(R))/A₀ + C_(ts)   p - The split candidate that yields minimal SAH   // split small nodes   if SAH_(p) ≧ SAH₀ then    Mark i as leaf node   else    Split i using p. add new nodes to nextlist    Sort triangles to new nodes end

The first procedure collects the split candidates, as generally represented at step 702 of FIG. 7. As generally represented at step 704, the preprocessing also generates the triangle sets contained in both sides of each splitting plane candidate with a single pass over the triangles in a node.

As generally represented in FIG. 8, the second procedure, PROCESSSMALLNODES, splits small nodes. Processed in parallel for each node i, the procedure (at step 802) gets its triangle set, triangleSet, and its uppermost ancestor, smallRoot, (also a small node) in the tree. Then the SAH costs for the splitting plane candidates located inside the node are computed (step 804). At step 806 the node is split using the optimal split plane with minimal cost, and triangles are sorted into child nodes (step 808). Instead of storing the triangle sets in the triangle-node association lists as is done in the large node stage, the triangle sets are stored in small nodes as a bitmask of its smallRoot, (step 810) as shown in FIGS. 9 and 10. Note that the triangle sets of each split candidate j, j.left and j.right, are also stored as bitmasks (e.g., 1010 and 1012). With this bitmask representation, triangle sorting and SAH evaluation for any split candidate can be efficiently done using bitwise operations.

As shown in Algorithm 4, the bitmask of the left child is computed as the bitwise AND of the bit mask of the current node s and the bit mask of the left side of the split candidate j, which is precomputed in PREPROCESSSMALLNODES. Then a known parallel bit counting routine is performed on the resulting bit mask to get the triangle number of the left child. The bit mask representation allows computing the optimal split plane in O(n) time and sort triangles in O(1) time. An alternative method for computing the optimal splitting plane in O(n) is to sort the split candidates in a preprocess. Then the cost functions of the split candidates and the optimal splitting plane can be computed by only a single pass over the sorted data, at the cost of O(n). However, since the sorted order cannot be represented as a bit mask, triangle sorting can only be done at the cost of O(n).

As described in the aforementioned related patent application, attorney docket no. 323434.01, one implemented GPU ray tracer is stack-based, requiring the kd-tree's final layout to be a preorder traversal of nodes for optimal cache performance. The preorder traversal is computed using two parallel breadth-first search traversals, e.g., as set forth in Algorithm 5 (PREORDERTRAVERSAL) and as represented in FIG. 11:

procedure PREORDERTRAVERSAL(nodelist:list) begin  for each tree level l of nodelist from bottom-up   UPPASS(l)  Allocate tree using root node's size  for each tree level l of nodelist from top-down   DOWNPASS(l) end procedure UPPASS(activelist:list) begin  for each node i in activelist in parallel   if i is not a leaf then    i.size ← i.left.size + i.right.size + 1   else    i.size ← i.triangleCount + 1 end procedure DOWNPASS(activelist:list) begin  for each node i in activelist in parallel   if i is not a leaf then    i.left.address ← i.address + 1    i.right.address ← i.address + 1 + i.left.size   Store node i in final format to i.address end

A first pass (step 1102) traverses the tree bottom-up to compute required memory size for each subtree. A second pass (step 1104) traverses the tree top-down to compute the starting address in the traversal for each subtree, and distributes node information to the corresponding address to produce the final tree. Note that the PREORDERTRAVERSAL algorithm collects nodes located at the same tree level. Further note that this information is already available in each while-loop in Algorithm 1.

After preorder traversal, each node in the resulting node list records the number and indices of the triangles it contains, its splitting plane, and the links to its children.

Exemplary Operating Environment

FIG. 12 illustrates an example of a suitable computing and networking environment 1200 on which the examples of FIGS. 1-11 may be implemented. The computing system environment 1200 is only one example of a suitable computing environment and is not intended to suggest any limitation as to the scope of use or functionality of the invention. Neither should the computing environment 1200 be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary operating environment 1200.

The invention is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well known computing systems, environments, and/or configurations that may be suitable for use with the invention include, but are not limited to: personal computers, server computers, hand-held or laptop devices, tablet devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.

The invention may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and so forth, which perform particular tasks or implement particular abstract data types. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in local and/or remote computer storage media including memory storage devices.

With reference to FIG. 12, an exemplary system for implementing various aspects of the invention may include a general purpose computing device in the form of a computer 1210. Components of the computer 1210 may include, but are not limited to, a processing unit 1220, a system memory 1230, and a system bus 1221 that couples various system components including the system memory to the processing unit 1220. The system bus 1221 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus also known as Mezzanine bus.

The computer 1210 typically includes a variety of computer-readable media. Computer-readable media can be any available media that can be accessed by the computer 1210 and includes both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, computer-readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by the computer 1210. Communication media typically embodies computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of the any of the above may also be included within the scope of computer-readable media.

The system memory 1230 includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) 1231 and random access memory (RAM) 1232. A basic input/output system 1233 (BIOS), containing the basic routines that help to transfer information between elements within computer 1210, such as during start-up, is typically stored in ROM 1231. RAM 1232 typically contains data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit 1220. By way of example, and not limitation, FIG. 12 illustrates operating system 1234, application programs 1235, other program modules 1236 and program data 1237.

The computer 1210 may also include other removable/non-removable, volatile/nonvolatile computer storage media. By way of example only, FIG. 12 illustrates a hard disk drive 1241 that reads from or writes to non-removable, nonvolatile magnetic media, a magnetic disk drive 1251 that reads from or writes to a removable, nonvolatile magnetic disk 1252, and an optical disk drive 1255 that reads from or writes to a removable, nonvolatile optical disk 1256 such as a CD ROM or other optical media. Other removable/non-removable, volatile/nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM, and the like. The hard disk drive 1241 is typically connected to the system bus 1221 through a non-removable memory interface such as interface 1240, and magnetic disk drive 1251 and optical disk drive 1255 are typically connected to the system bus 1221 by a removable memory interface, such as interface 1250.

The drives and their associated computer storage media, described above and illustrated in FIG. 12, provide storage of computer-readable instructions, data structures, program modules and other data for the computer 1210. In FIG. 12, for example, hard disk drive 1241 is illustrated as storing operating system 1244, application programs 1245, other program modules 1246 and program data 1247. Note that these components can either be the same as or different from operating system 1234, application programs 1235, other program modules 1236, and program data 1237. Operating system 1244, application programs 1245, other program modules 1246, and program data 1247 are given different numbers herein to illustrate that, at a minimum, they are different copies. A user may enter commands and information into the computer 1210 through input devices such as a tablet, or electronic digitizer, 1264, a microphone 1263, a keyboard 1262 and pointing device 1261, commonly referred to as mouse, trackball or touch pad. Other input devices not shown in FIG. 12 may include a joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the processing unit 1220 through a user input interface 1260 that is coupled to the system bus, but may be connected by other interface and bus structures, such as a parallel port, game port or a universal serial bus (USB). A monitor 1291 or other type of display device is also connected to the system bus 1221 via an interface, such as a video interface 1290. The monitor 1291 may also be integrated with a touch-screen panel or the like. Note that the monitor and/or touch screen panel can be physically coupled to a housing in which the computing device 1210 is incorporated, such as in a tablet-type personal computer. In addition, computers such as the computing device 1210 may also include other peripheral output devices such as speakers 1295 and printer 1296, which may be connected through an output peripheral interface 1294 or the like.

The computer 1210 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1280. The remote computer 1280 may be a personal computer, a server, a router, a network PC, a peer device or other common network node, and typically includes many or the of the elements described above relative to the computer 1210, although only a memory storage device 1281 has been illustrated in FIG. 12. The logical connections depicted in FIG. 12 include one or more local area networks (LAN) 1271 and one or more wide area networks (WAN) 1273, but may also include other networks. Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet.

When used in a LAN networking environment, the computer 1210 is connected to the LAN 1271 through a network interface or adapter 1270. When used in a WAN networking environment, the computer 1210 typically includes a modem 1272 or other means for establishing communications over the WAN 1273, such as the Internet. The modem 1272, which may be internal or external, may be connected to the system bus 1221 via the user input interface 1260 or other appropriate mechanism. A wireless networking component 1274 such as comprising an interface and antenna may be coupled through a suitable device such as an access point or peer computer to a WAN or LAN. In a networked environment, program modules depicted relative to the computer 1210, or portions thereof, may be stored in the remote memory storage device. By way of example, and not limitation, FIG. 12 illustrates remote application programs 1285 as residing on memory device 1281. It may be appreciated that the network connections shown are exemplary and other means of establishing a communications link between the computers may be used.

An auxiliary subsystem 1299 (e.g., for auxiliary display of content) may be connected via the user interface 1260 to allow data such as program content, system status and event notifications to be provided to the user, even if the main portions of the computer system are in a low power state. The auxiliary subsystem 1299 may be connected to the modem 1272 and/or network interface 1270 to allow communication between these systems while the main processing unit 1220 is in a low power state.

CONCLUSION

While the invention is susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover the modifications, alternative constructions, and equivalents falling within the spirit and scope of the invention. 

What is claimed is:
 1. In a computing environment, a method comprising, building a kd-tree via graphics hardware-based parallel processing, including spawning a thread for each node at a same tree level and building nodes of the kd-tree in breadth-first search order, and differentiating between large nodes and small nodes while building the kd-tree, including parallelizing computations over geometric primitives for large nodes at the same tree level.
 2. The method of claim 1 wherein differentiating between large nodes and small nodes comprises evaluating a number of triangles in a node relative to a threshold.
 3. The method of claim 1 wherein building nodes comprises recursively splitting a node into two sub-nodes.
 4. The method of claim 3 wherein the node is a large node, and wherein recursively splitting the node into two sub-nodes comprises cutting off space in a next split when sufficient empty space is contained in the node, or choosing a split plane at a spatial median when sufficient empty space is not contained in a node to be split.
 5. The method of claim 1 wherein at least one node is a large node, and wherein building the nodes of the kd-tree comprises, dividing triangles into chunks, computing a per-node bounding box, splitting a large node, sorting and clipping triangles to child nodes, and counting triangle numbers for the child nodes.
 6. The method of claim 5 further comprising, performing small node filtering on the child nodes based on the counting.
 7. The method of claim 1 wherein at least one node is a small node, and wherein building the nodes of the kd-tree comprises preprocessing each small node in a first procedure, and processing each small node in a second procedure.
 8. The method of claim 1 wherein preprocessing each small node comprises collecting split candidates, and generating a triangle set for sides of each split candidate.
 9. The method of claim 8 wherein processing each small node comprises getting a triangle set for the node, getting an uppermost ancestor, computing costs for split candidates corresponding to the node, and splitting based on computed costs.
 10. The method of claim 8 further comprising, representing triangle sets for candidates as bitmasks.
 11. The method of claim 10 further comprising, computing costs for split candidates based on the bitmasks.
 12. The method of claim 1 wherein building the kd-tree comprises, traversing the tree bottom-up to compute memory size for subtrees, traversing the tree top-down to compute a starting address in the traversal for each subtree, and distributing node information to the corresponding address to produce a final tree.
 13. In a computing environment having a graphics hardware, a system comprising, a kd-tree building mechanism coupled to the graphics hardware, including a mechanism configured to differentiate large nodes from small nodes based on triangles associated with each node, the kd-tree building mechanism configured to process nodes in breadth-first search order, including to generate a thread for each node to be represented by the kd-tree via parallel operations executed by the graphics hardware, including to split large nodes into child nodes by empty space splitting and spatial splitting, and to split small nodes into child nodes based on computed costs for split candidates.
 14. The system of claim 13 wherein empty space splitting comprises cutting off empty space when an empty space ratio is exceeded, and wherein spatial splitting comprises choosing a split plane at a spatial median of the node's longest axis split when the empty space ratio is not exceeded.
 15. The system of claim 13 further comprising a data structure coupled to the kd-tree building mechanism, the kd-tree building mechanism storing data corresponding to geometry primitives for the small nodes as bitmasks for computing the costs of the split candidates.
 16. One or more computer-readable storage media having computer-executable instructions stored thereon, which in response to execution by a computer, cause the computer to perform steps comprising, building a kd-tree via processing large nodes and small nodes in breadth-first search order, including spawning a thread for each node at a same tree level to perform at least some parallel operations on a graphics hardware, and including differentiating large nodes from small nodes based on triangles associated with each node, splitting large nodes into child nodes, parallelizing computations over geometric primitives for large nodes at upper tree levels, and splitting small nodes into child nodes based on computed costs for split candidates.
 17. The one or more computer-readable storage media of claim 16 wherein splitting large nodes into child nodes comprises cutting off empty space based until a empty space ratio is achieved, and thereafter performing spatial splitting.
 18. The one or more computer-readable storage media of claim 16 wherein splitting small nodes into child nodes comprises computing costs for split candidates corresponding to each child node, including computing via a surface area heuristic or a voxel volume heuristic. 